在决策科学中，线性不等式组是一种基本的数学结构，它的化简很有实用价值。
The system of linear inequalities is a fundamental mathematical structure in decision theory.
运用多项式稳定性充分判据，将线性系统的同时镇定问题转化成非线性不等式组的求解。
In this paper, the simultaneous stabilization problem of linear systems is transformed into solving problems of a set of nonlinear inequalities by using a sufficient criterion of polynomial stability.
从而使问题转化成求解二元线性不等式组的问题，为此可方便地借助计算机求出最佳结果。
The problem is changed to solving the linear inequality group with two unknown, thus, we can get the optimal solution by the computer.
它在理论上是多项式算法，并可以从任意点启动，可以应用共轭梯度方法有效地求解大规模线性不等式组问题。
SDNM is a polynomial time algorithm with the Newtons method, so that SDNM can solve large-scale linear inequalities.
采用引进具有二阶连续可微的辅助函数，将非线性不等式组转化为非线性方程组，然后利用牛顿迭代法对非线性方程组进行求解。
In is established the equivalence between the nonlinear inequalities with nonlinear equations by using auxiliary function, a descended Newton algorithm is proposed.
所运用的线性不等式组的一种旋转算法避免了通常处理二次规划问题所需的松弛变量、剩余变量和人工变量，操作简便、计算效率高。
The algorithm solves the quadric programming problem without adding slack, remaining and artificial variables while its efficiency is very high and it operates very easily.
假定所要设计的控制器存在状态反馈增益变化，设计方法是以线性矩阵不等式组的形式给出的。
The controller to be designed is assumed to have state feedback gain variations. Design methods are presented in terms of linear matrix inequalities (LMIs).
以周期非线性光学介质中隙孤子存在的条件为依据，数学计算分析得到两组参量关系不等式。
Based on the conditions of the gap soliton in periodical nonlinear optical medium, two inequalities for relation of parameters are obtained.
控制器的所有参数可以通过求解一组线性矩阵不等式得到。
All the parameters of the controllers can be obtained by solving a linear matrix inequality.
利用齐次线性方程组解的理论讨论矩阵的秩，给出几个关于矩阵秩的著名不等式的证明，并证明了两个命题。
The article discusses rank of a matrix by the solution theorem of system of homogeneous linear equations, and proves several famous inequalities and two propositions on rank of a matrix.
本文主要讨论求解非线性方程组问题与变分不等式问题的迭代算法。全文共分三章。
This thesis includes three chapters, which mainly discusses the iterative algorithms for solving nonlinear equations problems and nonlinear variational inequality problems.
第四章给出了求解线性丢番图不等式组的ABS算法及其在整线性规划中的应用。
Chapter four gives ABS algorithms for solving linear Diophantine inequations and their application in integer linear programming.
第五章给出了求解超定线性丢番图方程组和不等式组的修正abs算法。
Chapter five presents the modified ABS algorithms for solving linear overdetermined linear Diophantine equations and inequations.
讨论了一类非线性等式与不等式组的相容性，给出了其相容的充要条件。
The compatibility of a class of nonlinear equality and inequality systems is discussed. The necessary and sufficient conditions of the compatibility are given.
控制器的设计可以通过求解一组线性矩阵不等式(LMI)得到。
本文以两个自变量的拟线性双曲型方程的古尔沙问题为例，应用反函数和积分不等式证明了等价积分方程组解的存在唯一性，同时给出了解的存在区域和已知参量的依赖关系。
In this paper, we show the domain of the existence of the solution on Goursat problem for quasi—linear hyperbolic equation and obtain the Theorem of the existence and uniqueness in above domain.
带不等式约束的非线性规划，其KKT条件可以通过NCP函数转化为一个非光滑的方程组，然后用熵光滑化函数光滑化，得到一个带参数的方程组。
The KKT conditions of a nonlinear programming with linear inequality constrains can be transformed into a system of equations by NCP function. Then it is smoothed by Entropy smoothing function.
利用齐次线性方程组解的理论讨论矩阵的秩，给出几个关于矩阵秩的著名不等式的证明，并证明了两个命题。
The judgment theorems for locating correctness were concluded by skillfully combining the solutions of homogenous linear equations with locating schemes.
利用齐次线性方程组解的理论讨论矩阵的秩，给出几个关于矩阵秩的著名不等式的证明，并证明了两个命题。
The judgment theorems for locating correctness were concluded by skillfully combining the solutions of homogenous linear equations with locating schemes.
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